There are a number of signal analysis techniques which involve detecting level-crossings, and particularly zero-crossings. For example, polarity coincidence correlation is a technique which has been well-known for a long time (see, for example, Helmut Bemdt, “Correlation Function Estimation by a Polarity Method Using Stochastic Reference Signals”. IEEE Transactions on Information Theory, vol. 14, No. 6, Nov. 1968, pp. 796-801).
A more recent example is disclosed in WO-A-00/39643 (incorporated herein by reference). This describes a method of detecting the shift between two irregular signals, one of which is a copy of the other, by detecting non-uniformly spaced zero-crossings in a first signal, and using these to trigger the sampling of the second signal. The system introduces different delays between the zero-crossings and the sampling time. For each respective delay value, the samples are summed. For most delays, the summed samples will represent an average signal value. However, when the delay is close to a value which matches the shift between the signals, the summed samples become coherent, giving rise to a distinctive feature in the system output. FIG. 1 shows a typical output, with the horizontal axis representing the introduced delay between the detected zero-crossing and the sampling of the second signal. The S-shaped odd function clearly shown therein is located at a position corresponding to the time shift between the two signals.
This method will be referred to as “crosslation”, and a system implementing the method will be referred to as a “crosslator”. Such techniques can be used for object detection, for example by transmitting a wideband, noise-like irregular signal, and measuring the delay between that signal and a reflection of the signal from an object.
As explained in WO-A-00/39643, the detected zero-crossings may be those which occur when the signal level crosses zero with a positive slope (upcrossings), those which occur when the level crosses zero with a negative slope (downcrossings), or both. If both upcrossings and downcrossings are used, the summed samples defined by upcrossings are subtracted from those defined by downcrossings.
In WO-A-00/39643, a shift register produces multiple versions of the second signal, the versions being delayed by different amounts. Each zero-crossing simultaneously triggers the sampling of these different versions. FIG. 2 shows another form of crosslator for measuring time delay in an object detection and ranging system. In the FIG. 2 system, the values derived by combining the samples of the second signal are obtained in succession for respective different delays, rather than simultaneously. In FIG. 2, the second signal y(t) is converted by a hard limiter HY into a corresponding binary bipolar waveform. This waveform and its polarity-reversed replica are supplied to an averaging or integrating unit AVG via a switch. The switch is normally open but supplies the output or its polarity-reversed replica to unit AVG when a zero-crossing detector ZCD detects, respectively, an upcrossing or a downcrossing in the first signal x(t). The signal x(t) has been processed by a hard limiter HX and then delayed by a variable delay line VD. After a predetermined time interval has elapsed (or when a predetermined condition is met, such as the number of zero-crossings reaching a predetermined value), the output of unit AVG is delivered to a data processor DPR. This output will represent one point on the function illustrated in FIG. 1. The data processor DPR sets the delay introduced by the variable delay line VD to a different value, and then repeats the operation, to derive a further point on the function. By comparing the different values obtained from the unit AVG for different delays, the data processor DPR can determine the delay between the signals x(t) and y(t). The variable delay line VD could instead be placed in the path of the signal y(t), the signal x(t) being subjected to a suitable constant delay. In another modification, the hard limiter HY is omitted and the unit AVG operates directly on the analog values of the signal y(t). Furthermore, a monitoring system can be obtained by using a fixed delay in place of the variable delay line VD, whereby the system can be used to monitor whether the range of an object departs from a particular distance corresponding to the value of that fixed delay.
The shift between the two signals may represent time, as in the object detection and ranging system mentioned above, or may represent another parameter, such as linear or angular shift. In one specific example, a first signal may represent an image, for example a line through a two-dimensional video image. A second signal may represent a second version of the image, which is linearly shifted (translated) with respect to the first. Each signal could for example be a grey scale representation of a line across a video screen. One of the signals can be processed so as to obtain successive points each representing the intersection of the grey scale waveform with a particular reference level. These points can then be used for the sampling of different versions of the second signal, each version being associated with a different linear shift. The amount of image movement can thus be determined by using the crosslation technique mentioned above.
Another example of signal analysis which involves the use of zero-crossing detection is shown in EP-A-1378854 (incorporated herein by reference). Here a crosslation technique is used to derive information about a signal, for example to classify images or sounds or other physical phenomena represented by the signal. In this case, the zero-crossings detected in the signal are used to trigger the sampling of the same signal. A delay is introduced between the occurrence of each zero-crossing and the sampling of the signal. The samples are combined to get a first value. The operation is repeated with different delays to produce other values. The multiple values derived using the different delays form a representation of the original signal, and the shape of this representation indicates a statistical characteristic of the signal.
A further technique involving level-crossing detection is disclosed in WO-A-03/036564 (incorporated herein by reference). An image is analysed by using a mapping function to derive a one-dimensional representation of the image, the representation having a varying level, and by determining (a) the rate at which the level crosses one or more thresholds, (b) the average slope of the signal when it crosses one or more threshold levels, and/or (c) the average duration for which the signal remains above one or more threshold levels.
The performance of the systems mentioned above is impaired by noise and other interfering signals. Because unwanted signals are not related functionally or statistically to the irregular signal being processed, the efficacy of interference suppression will increase with the number of level-crossings in the signal. Taking the crosslation technique of WO-A-00/39643 as an example, the number of averaged segments of a received signal y(t) is determined by the number of significant events (zero-crossings) extracted from a transmitted random signal x(t). Therefore, it would be desirable to determine an optimum number of signal segments of y(t) which need to be averaged in time T to provide maximum interference suppression.
It is known, by the sampling theorem, that a wideband random signal is completely determined by its samples taken uniformly at time instants separated by the interval 1/(2W), where W is the highest frequency component of the signal's power spectrum. This result is often stated that a noise waveform of duration T contains Λ=2WT degrees of freedom.
In signal processing applications, the product Λ is also referred to as the processing gain, because it indicates the bound on the achievable reduction of noise power by averaging uncorrelated samples of a respective noise waveform. It is also known that the above results apply to cases when a noise waveform is sampled in a non-uniform manner, yet with the mean sampling rate of 2W samples per second.
From the above discussion it follows that the ability of a processor operating on zero-crossings to suppress unwanted interference can be degraded when the number of zero-crossings extracted from a transmitted wideband signal x(t) is less than Λ. This conclusion will be explained in more detail by way of the following example.